Relaxed Kačanov Scheme for the \(\boldsymbol{p}\)-Laplacian with Large Exponent
Anna Kh. Balci, Lars Diening, Johannes Storn · SIAM Journal on Numerical Analysis · 2023
Abstract. We introduce a novel relaxed Kačanov scheme for the computation of the discrete minimizer to the [Formula: see text]-Laplace problem with [Formula: see text]. The iterative scheme is easy to implement since each iterate results only from the solve of a weighted, linear Poisson problem. It neither requires an additional line search nor involves unknown constants for the step length. The scheme converges globally, and its rate of convergence is independent of the underlying mesh under certain regularity assumptions on the (discrete) solution.